Higher-order and crystalline topology in a phenomenological tight-binding model of lead telluride

In this work, we revisit the model of PbTe presented by Fradkin et al. [Phys. Rev. Lett. 57, 2967 (1986)]. We show that the low-energy theory of this model corresponds to a (higher-order) topological crystalline insulator in space group Fm (3) over bar m1', diagnosable by symmetry indicators. We show that the gapless fermions found on antiphase domain walls are the topological boundary modes of the system, due to a nonvanishing mirror Chern number. Furthermore, we show that any symmetric completion of the model must be in this same topological phase. Finally, we comment on the relationship of this model to realistic PbTe, which has recently been predicted to have a phase which realizes same bulk symmetry indicators.